Adaptive Near-Optimal Control Using Sliding Mode

Abstract

In this chapter, an adaptive near-optimal controller, which is inherently real time, is designed to tackle the contradictory between solution accuracy and solution speed for the optimal control of a general class of nonlinear systems with fully unknown parameters. The key technique in the presented adaptive near-optimal control is to design an auxiliary system with the aid of the sliding mode control concept to reconstruct the dynamics of the controlled nonlinear system. Based on the sliding-mode auxiliary system and approximation of the performance index, the presented controller guarantees asymptotic stability of the closed-system and asymptotic optimality of the performance index with time. Two illustrative examples and an application of the presented method to a van der Pol oscillator are presented to validate the efficacy of the presented adaptive near-optimal control. In addition, physical experiment results based on a DC motor are also presented to show the realizability, performance, and superiority of the presented method.